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PHYSICS 251: TEST 2 3/2/16 Dr. Varriano NAME:_____________________________ Do all 7 problems. Show all of your work in the space provided to receive partial credit. You may use additional sheets of paper if necessary. Put your final answer to each question on the line provided unless instructed otherwise. ___________________________________________________________________________ 1. [14 pts] There are two point charges in the xy-plane, a -9 nC charge at the origin and a +9 nC charge located on the x-axis at (4 cm, 0). Points A through C are located at the following coordinates: A (1cm, 0) B (2 cm, 0) C (3 cm, 0) (a) Is the net voltage at point A positive, negative, or zero? (Circle the correct choice.) positive negative zero (b) Is the net voltage at point B positive, negative, or zero? (Circle the correct choice.) positive negative zero (c) Is the net voltage at point C positive, negative, or zero? (Circle the correct choice.) positive negative zero (d) Find the value of the net voltage at point A. -5400 V (e) Find the potential energy of the pair of charges. -18.2 nJ 2. [14 pts] The voltage at some point in space (point A) is -15 Volts. The voltage at another point in space (point B) is -10 Volts. A -2 nC charged particle is observed to travel from A to B. During this time, the only force acting on it is the electric force. (a) Compared to its speed at point A, is this particle moving faster, slower, or at the same speed when it arrives at point B? faster (b) What is the particle’s potential energy at point A? +30 nJ (c) Find the change in the particle’s kinetic energy in going from A to B. +10 nJ 3. [14 pts] My toaster, plugged into a standard outlet that delivers 120 V, uses 1000 W of power when toasting my bagel in the morning. (a) How much current does the toaster draw? 8.3 A (b) What is the resistance of the heating element in the toaster? 14.4 Ω (c) How much energy does the toaster use if it takes 1 minute for my bagel to be just right? (Answer in Joules or kilowatt-hours.) 60 kJ 2 4. [14 pts] A battery charges up a 5-F capacitor. The battery is removed. The capacitor stores 90 J of energy and the electric field points from the bottom plate to the top plate. (a) Find the voltage difference between the plates of the capacitor. 6V (b) How much net charge is stored on the plates of this capacitor (sign and size)? Top plate -30 μC Bottom plate +30 μC (c) Suppose the capacitor is discharged and then again charged up with a different battery with a lower voltage difference. Circle the correct word choice in the parentheses to make each statement correct. The charge moved by this battery is ( greater than / less than / the same as ) the charge moved by the first battery. The capacitance of the capacitor is ( larger than / smaller than / the same as ) it was before. 5. [15 pts] You have three 3-F capacitors and a 10-V battery. (a) Sketch below how to hook all of them together to the battery to get an equivalent capacitance of exactly 4.5 F for the circuit. 10 V Put two in series with the battery. Then connect the last one to the battery terminals. (b) Which of the following statements are true when the correct circuit is built? (Circle the number(s) before the true statement(s). There may be more than one true statement.) 1. 2. 3. 4. 5. The battery moves a total of 45 C of charge. Each capacitor stores 45 C of charge. One capacitor has a 10 V difference across its plates. All three capacitors are in series. The battery does 225 J of work in charging up the capacitors. 3 7. [15 pts] Consider the circuit shown. The equivalent resistance of the circuit is 500 . (a) Find the resistance R . __500 Ω (b) Find the total current flowing from the battery. 20 mA (c) How much of this total current goes through the 2000- resistor? 4 mA 8. [14 pts] Consider the two parallel plates in the sketch below. Electrons are accelerated from rest to a speed of 8x106 m/s as they travel from the left plate to the right plate. An electron is shown in between the plates in the sketch (a) On the sketch, label the plate at the higher voltage with a '+' and the plate at the lower voltage with a '-'. (b) On the sketch, draw an arrow between the plates representing the direction of the electric field. (c) On the sketch, draw an arrow from the electron representing the direction of the force on the electron. (d) What is the voltage difference between the plates? 182 V (e) The voltage difference across the plates is decreased. What happens to the following quantities? (Circle the correct choice.) final speed of electrons increases decreases remains the same electric field between plates increases decreases remains the same